Data in 1980 showed that about 40% of the adult population had never smoked cigarettes.In 2004, a national health survey interviewed a random sample of 2000 adults and found that 50% had never been smokers.Create a 95% confidence interval for the proportion of adults (in 2004) who had never been smokers.
A)Based on the data, we are 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between 47.8% and 52.2%.
B)Based on the data, we are 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between 37.4% and 52.2%.
C)Based on the data, we are 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between 47.8% and 58.2%.
D)Based on the data, we are 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between 40% and 60%.
E)Based on the data, we are 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between 47.8% and 63.2%.

Question

Quizplus · Accepted Answer

To calculate the 95% confidence interval for the proportion of adults who had never been smokers, we use the formula for the confidence interval of a proportion: $p \pm z\sqrt{\frac{p(1-p)}{n}}$, where $p$ is the sample proportion (0.50), $n$ is the sample size (2000), and $z$ is the z-score corresponding to the 95% confidence level (approximately 1.96). Plugging in the values, we get the interval $[0.478, 0.522]$, or 47.8% to 52.2%.

Data in 1980 Showed That About 40% of the Adult